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Question

A cube is located such that its top four corners have the coordinates (−1,−1,3), (−1,7,3), (7,−1,3) and (7,7,3). Give the coordinates of the center of the cube.

Answer 1

The top four points of the cube are (−1,−1,3), (−1,7,3), (7,−1,3) and (7,7,3)

They have the same z-coordinate: z = 3.

The x-coordinates range from −1 to 7

The y-coordinates range from −1 to 7

This tells us three things:

1. The length of each side is 8 (since 7 – (–1) = 8)
2. The average value of the x-coordinates is x_avg = 3 (since (7 – 1)/2 = 3)
3. The average value of the y-coordinates is y_avg = 3 (since (7 – 1)/2 = 3)

Since the length of each side is 8, this means that

1. The z-coordinate of each of the four bottom corners is 3 – 8 = –5
2. The average value of the z-coordinates is z_avg = –1 (since (3 – 5)/2 = –1)

The coordinates of the center of the cube are just

the average of each of the coordinates ( x_avg, y_avg, z_avg)

Answer

The coordinates of the center of the cube are (3, 3, –1)